Page 153 - Industrial Ventilation Design Guidebook

4,3 HEAT AND MASS TRANSFER I I 5

This equation does not incorporate the characteristic length L; hence the wall
height has no influence on heat transfer.
In problems of forced convection, it is usually the cooling mass flow that
has to be found to determine the temperature difference between the cooling
substance and the wall for a given heat flow. In turbulent pipe flow, the fol-
lowing equation is valid:

The mass flow is found using the continuity equation m — pwird /4 and the
Reynolds number formula Re = 4m/(Trp dv)\

In some convection equations, such as for turbulent pipe flow, a
special correction factor is used. This factor relates to the heat transfer
conditions at the flow inlet, where the flow has not reached its final ve-
locity distribution and the boundary layer is not fully developed. In this
region the heat transfer rate is better than at the region of fully devel-
oped flow.
The reason the heat transfer is improved can be seen from the equations
Nu = as/A (where s is the thickness of the boundary layer) and q = «0,
giving

Thin boundary layers provide the highest values of heat flow density. Be-
cause the boundary layer gradually develops upstream from the inlet
point, the heat flow density is highest at the inlet point. Heat flow density
decreases and achieves its final value in the region of fully developed flow.
The correction is noted in the equations by means of the quotients d/L
and d/x.
For some fluids, such as oils, the viscosity is temperature dependent. Here
the correction factor (f]f/r\ w} ' is used, where ^p is the viscosity at the mean
fluid temperature and r\ w is the viscosity at the wall temperature.

4.3.3.4 Forced Convection
In this section the correlations used to determine the heat and mass
transfer rates are presented. The convection process may be either free or
forced convection. In free convection fluid motion is created by buoyancy
forces within the fluid. In most industrial processes, forced convection is
necessary in order to achieve the most economic heat exchange. The heat
transfer correlations for forced convection in external and internal flows
are given in Tables 4.8 and 4.9, respectively, for different conditions and
geometries.
The mass transfer correlations are obtained by replacing Nu by Sh and Pr
by Sc according to the heat and mass transfer analogy.